Question

A tailor makes two types of garments A and B. Garment A requires 3 metres of material while garment B requires 2 ½ metres of material. The tailor uses not more than 600 metres of material daily in making both garments. He must make not more than 100 garments of type A and not less than 80 of type B each day.

1. Write down all the inequalities from this information. 
2. Graph the inequalities above 
3. If the business makes a profit of shs. 80 on garment A and a profit of shs. 60 on garment B, how many garments of each type must it make in order to maximize the total profit?

Answer 1

1. Write down all the inequalities from this information.
   (i) 3x + 2 1/2y ≤ 600
   (ii) x ≤ 100
   (iii) Y ≥ 80, x ≥ 0
    
2. Graph the inequalities above 
   
   line 3x + 2 1/2y ≤ 600
   Line x ≤ 100
   Line ≥ 80, x ≥ 0
    
3. If the business makes a profit of shs. 80 on garment A and a profit of shs. 60 on garment B, how many garments of each type must it make in order to maximize the total profit? 
   The objective functions
   P = 80x + 60y
   100 garments of type A
   120 garments of type B